Question

How do you simplify $\dfrac{3}{5} - \dfrac{5}{{10}}$ ?

Answer 1

Hint:We are given two fractions that are in subtraction and we know that when two fractions are linked via some arithmetic operation like addition or subtraction, then we have to first make their denominator equal. For that, we will find the least common multiple (LCM) of the denominators and then we multiply the numerator of each fraction with the quotient obtained on dividing the LCM by their denominators. This way we will get the simplified form of the given expression.

Complete step-by-step solution:
We have to simplify $\dfrac{3}{5} - \dfrac{5}{{10}}$
5 and 10 are the denominators of the two fractions.
On the prime factorization of 5 and 10, we see that –
$
  \Rightarrow 5 = 1 \times 5 \\
  \Rightarrow 10 = 2 \times 5 \\
 $
The LCM of 5 and 10 is $2 \times 5 = 10$ .
The quotient obtained on dividing 10 by 5 is 2 and the quotient obtained on dividing 10 by 10 is 1. So, we multiply the numerator of 5 by 2 and the numerator of 10 by 1 –
$
   \Rightarrow \dfrac{3}{5} - \dfrac{5}{{10}} = \dfrac{{3 \times 2 - 5 \times 1}}{{10}} \\
   \Rightarrow \dfrac{3}{5} - \dfrac{5}{{10}} = \dfrac{{6 - 5}}{{10}} \\
   \Rightarrow \dfrac{3}{5} - \dfrac{5}{{10}} = \dfrac{1}{{10}} \\
 $
Hence, the simplified form of $\dfrac{3}{5} - \dfrac{5}{{10}}$ is $\dfrac{1}{{10}}$ or $0.1$ .

Note: A fraction is a mathematical expression in which two numbers are divided by a horizontal line, the number on the upper side of the horizontal line is called the numerator and the number on the lower side of the horizontal line is called the denominator. The obtained fraction is already in simplified form; otherwise, we would express the numerator and the denominator of the fraction as a product of its prime factors and then cancel out the common factors.